Subgroups — C₄×Dic₃×D₁₃ #11928515

Order 1248.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×D₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₃×D₁₃	C₂	1	2	yes	maximal
3	C₄×Dic₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×Dic₃×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
5	Dic₃×Dic₁₃	C₂	1	2	yes	maximal, complemented
6	C₄²×D₁₃	—	3	1	no	maximal, Hall
7	C₂²×C₃×D₁₃	C₂²	1	1	yes	characteristic
8	C₂×C₃×C₄×C₁₃	C₂²	1	1	yes	characteristic
9	C₂×Dic₃₉	C₂²	1	2	yes	—
10	C₂×Dic₃×C₁₃	C₂²	1	2	yes	—
11	C₂×C₃×Dic₁₃	C₂²	1	1	yes	characteristic
12	C₃×C₄×D₁₃	C₄	1	4	yes	complemented
13	Dic₃×D₁₃	C₄	1	8	yes	direct product factor
14	C₂×C₄×D₁₃	—	3	2	no	—
15	C₂×C₄×D₁₃	D₃	1	1	yes	characteristic
16	C₄²×C₁₃	—	3	1	no	—
17	C₄×Dic₁₃	—	3	1	no	—
18	C₄×Dic₁₃	—	3	2	no	—
19	C₂²×C₃×C₁₃	C₂³	1	1	yes	characteristic
20	C₂×C₃×D₁₃	C₂×C₄	1	4	yes	—
21	C₂×C₃×D₁₃	C₂×C₄	1	2	yes	—
22	C₃×C₄×C₁₃	C₂×C₄	1	2	yes	complemented
23	Dic₃₉	C₂×C₄	1	4	yes	complemented
24	C₃×Dic₁₃	C₂×C₄	1	2	yes	complemented
25	Dic₃×C₁₃	C₂×C₄	1	4	yes	complemented
26	C₂²×D₁₃	C₂×D₃	1	1	yes	characteristic
27	C₂×C₄×C₁₃	—	3	2	no	—
28	C₂×C₄×C₁₃	C₂×D₃	1	1	yes	characteristic
29	C₂×Dic₁₃	—	3	2	no	—
30	C₂×Dic₁₃	C₂×D₃	1	1	yes	characteristic
31	C₄×D₁₃	—	3	8	no	—
32	C₄×D₁₃	Dic₃	1	4	yes	direct product factor
33	C₂×C₄×Dic₃	—	13	1	no	maximal, Hall
34	C₂×C₃×C₁₃	C₂²×C₄	1	2	yes	—
35	C₂×C₃×C₁₃	C₂²×C₄	1	1	yes	characteristic
36	C₃×D₁₃	C₄²	1	4	yes	complemented
37	C₂²×C₁₃	C₂²×D₃	1	1	yes	characteristic
38	C₂×D₁₃	C₄×D₃	1	4	yes	—
39	C₂×D₁₃	C₂×Dic₃	1	2	yes	—
40	C₄×C₁₃	—	3	4	no	—
41	C₄×C₁₃	C₂×Dic₃	1	2	yes	complemented
42	Dic₁₃	—	3	4	no	—
43	Dic₁₃	C₂×Dic₃	1	2	yes	complemented
44	C₂²×C₃×C₄	—	13	1	no	—
45	C₂²×Dic₃	—	13	2	no	—
46	C₄×Dic₃	—	13	1	no	—
47	C₄×Dic₃	—	13	2	no	—
48	C₄×Dic₃	D₁₃	1	1	yes	characteristic, direct product factor
49	C₃×C₁₃	C₂×C₄²	1	1	yes	characteristic, complemented, Hall
50	C₂×C₄²	—	39	1	no	Sylow
51	C₂×C₁₃	C₂×C₄×D₃	1	2	yes	—
52	C₂×C₁₃	C₂²×Dic₃	1	1	yes	characteristic
53	D₁₃	C₄×Dic₃	1	4	yes	direct product factor
54	C₂³×C₃	—	13	1	no	—
55	C₂×C₃×C₄	—	13	1	no	—
56	C₂×C₃×C₄	—	13	4	no	—
57	C₂×C₃×C₄	C₂×D₁₃	1	1	yes	characteristic
58	C₂×Dic₃	—	13	2	no	—
59	C₂×Dic₃	—	13	8	no	—
60	C₂×Dic₃	C₂×D₁₃	1	2	yes	—
61	C₂²×C₄	—	13	1	no	—
62	C₂²×C₄	—	39	2	no	—
63	C₄²	—	3	1	no	—
64	C₄²	—	39	2	no	—
65	C₄²	—	39	1	no	—
66	C₁₃	C₂×C₄×Dic₃	1	1	yes	characteristic, complemented, Sylow
67	C₂²×C₃	—	13	4	no	—
68	C₂²×C₃	—	13	2	no	—
69	C₂²×C₃	C₂²×D₁₃	1	1	yes	characteristic
70	C₃×C₄	—	13	2	no	—
71	C₃×C₄	C₄×D₁₃	1	2	yes	complemented
72	Dic₃	—	13	4	no	—
73	Dic₃	C₄×D₁₃	1	4	yes	direct product factor
74	C₂³	—	13	1	no	—
75	C₂×C₄	—	3	2	no	—
76	C₂×C₄	—	13	1	no	—
77	C₂×C₄	—	13	4	no	—
78	C₂×C₄	—	39	8	no	—
79	C₂×C₄	—	39	2	no	—
80	C₂×C₄	D₃×D₁₃	1	1	yes	characteristic
81	C₂×C₃	—	13	4	no	—
82	C₂×C₃	C₂×C₄×D₁₃	1	2	yes	—
83	C₂×C₃	C₂×C₄×D₁₃	1	1	yes	characteristic
84	C₂²	—	13	4	no	—
85	C₂²	—	13	2	no	—
86	C₂²	C₂×D₃×D₁₃	1	1	yes	characteristic
87	C₄	—	3	4	no	—
88	C₄	—	13	2	no	—
89	C₄	—	39	4	no	—
90	C₄	Dic₃×D₁₃	1	2	yes	direct product factor
91	C₃	C₄²×D₁₃	1	1	yes	characteristic, complemented, Sylow
92	C₂	—	13	4	no	—
93	C₂	C₄×D₃×D₁₃	1	2	yes	—
94	C₂	C₂×Dic₃×D₁₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₄	D₃×D₁₃
commutator, hypocenter	C₃×C₁₃	C₂×C₄²
Frattini	C₂²	C₂×D₃×D₁₃
Fitting	C₂×C₃×C₄×C₁₃	C₂²
socle, cosocle	C₂²×C₃×C₁₃	C₂³
prime radical	C₂²×C₃×D₁₃	C₂²
LCS	G ▷ C₃×C₁₃
UCS	C₁ ◁ C₂×C₄

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
3. C₄×Dic₃₉	C₂	semidirect
4. C₄×Dic₃×C₁₃	C₂	semidirect
5. Dic₃×Dic₁₃	C₂	semidirect
12. C₃×C₄×D₁₃	C₄	semidirect
13. Dic₃×D₁₃	C₄	direct (N × H)
22. C₃×C₄×C₁₃	C₂×C₄	semidirect
23. Dic₃₉	C₂×C₄	semidirect
24. C₃×Dic₁₃	C₂×C₄	semidirect
25. Dic₃×C₁₃	C₂×C₄	semidirect
32. C₄×D₁₃	Dic₃	direct (N × H)
36. C₃×D₁₃	C₄²	semidirect
41. C₄×C₁₃	C₂×Dic₃	semidirect
43. Dic₁₃	C₂×Dic₃	semidirect
48. C₄×Dic₃	D₁₃	direct (N × H)
49. C₃×C₁₃	C₂×C₄²	semidirect
53. D₁₃	C₄×Dic₃	direct (N × H)
66. C₁₃	C₂×C₄×Dic₃	semidirect
71. C₃×C₄	C₄×D₁₃	semidirect
73. Dic₃	C₄×D₁₃	direct (N × H)
90. C₄	Dic₃×D₁₃	direct (N × H)
91. C₃	C₄²×D₁₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃×C₄×D₁₃	2
C₂×Dic₃×D₁₃	2
C₄×Dic₃₉	2
C₄×Dic₃×C₁₃	2
Dic₃×Dic₁₃	2
C₄²×D₁₃	3
C₂×C₄×Dic₃	13

Subgroups — C4×Dic3×D13 #11928515

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×Dic₃×D₁₃ #11928515